EXERCISE 3 (6 pt.): Computational Nuclear Physics NASAs Cassini Spacecraft uses the heat from the decay of Plutonium-238 (Pu-238) to generate electric power during Cassinis journey to Saturn. Cassini uses 3 Radioisotope Thermoelectric Generators (RTG for short) fueled with Plutonium-238 and Plutonium-241 to generate the electric power[1]. Pu-238 & Pu-241 are alpha emitters and are NOT the type of Pu used in nuclear weapons. The below table is a listing of the quantities of 3 isotopes making the most thermal power in each RTG. Assume that the readings were taken 1 year before launch.

NOTE: This is an actual problem calculated by the US Department of Energy and NASA in designing the power requirements during the mission of the Cassini Spacecraft which launched in 1996. The quantity of the Pu-238 & Pu-241 are the actual values reported at launch. There are other radioactive isotopes in the RTG, but for this problem, we are ignoring them.

The 4 elements that we are including are 2 isotopes of Plutonium [Pu-238 an alpha decay radioactive isotope] and [Pu-241 a beta decay radioactive isotope], one isotope of Americanium [Am-241 another alpha decay isotope], and two isotopes that we will assume (for this exercise) are stable and do not decay: Uranium (U-234) and Neptunium [Np-241]. By the way, Pu-237 is the stuff that explodes violently, we will NOT be using that element on a NASA mission!

Isotope	Weight (grams)	Thermal Output Ratio [Watts/gram]	Half Life []	Decays to
Pu-238 [Plutonium]	7693.7	0.5667	86 years	U-234 (assume stable)
Pu-241	20.2	0.2970	13.2 years	Am-241
Am-241 [Americium]	10.0	0.3000	4.58 years	Np-237 (assume stable)

Radioactive materials decay by the following formula:

(Equation 12-1)

where N(t) is the weight of the atoms (in grams) at time=t and ?t = 1

NOTES:

is the same as the (1-DeathRate)multiplier that we used in population models

To find the thermal output from each radioactive element, multiply the weight times the ratio in the table above.

To find the TOTAL thermal output, add the thermal outputs from each element together. The thermal output of U-234 & Np-237 is 0 watts because it is stable.

Question 1: First develop on paper, a MATLAB code that will calculate the decay of the elements and the amount of thermal output produced. Turn this in.

Question 2: Enter the program into MATLAB and calculate the quantity of Pu-238, Pu-241, and AM-241 at the endof each year for the next 15 years (t+1=16 years). Turn in a screenshot.

Question 3: Compute the total thermal output for the time period in Question #2 and plot the total thermal output vs time. Turn in a plot.

[1]Cassini Safety Evaluation Report by the Interagency Nuclear Safety Review Panel, J.Lyver, NASA INSRP Coordinator, Lead/Editor, 1996